C₂×C₅₃×#2029 #27230977

order	13568
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₅₃×#2029

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₅₃
prime radical	C₂⁶×C₅₃	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂⁵×C₅₃ ◁ G

2818 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 350 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1696

A minimal faithful permutation representation — 4 generators on 71 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55);(56,57,59,61)(58,62,63,60)(64,65)(66,68)(67,69)(70,71);(56,58,59,63)(57,60,61,62)(64,66)(65,68)(67,70)(69,71);(68,71)

Conjugacy classes & character table

2756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 16453);